Suppose that you are considering buying a house for $$250,000.$ You have found a bank that is willing to provide you with a $30-$year mortgage for $85\%$ of the purchase price with an annual interest rate of $8\%$ with monthly payments and compounding.

a$.$ What will be the monthly payment for this loan?

b$.$ What will the balance on this loan be at the end of the $9^{th}$ year?

c$.$ How much interest will you pay in the first year of this loan?

d$.$ How much principal will you pay in the ${13}^{th}$ year of this loan?

e$.$ How much interest will you pay in the first $5$ years of this loan?